Linear.Mat

Documentation

data M2 a

The components are row vectors

Constructors

M2 !(V2 a) !(V2 a)

Instances

Num a => Vector a M2

Fractional a => Orthogonal a M2 Ortho2

Num a => Extend a M2 M4

Num a => Extend a M2 M3

Fractional a => Projective a V2 M2 Ortho2 M3 Proj3

Num a => Determinant a (M2 a)

Floating a => MatrixNorms a (M2 a)

Read a => Read (M2 a)

Show a => Show (M2 a)

(Num a, Storable a) => Storable (M2 a)

(Num a, Random a) => Random (M2 a)

Num a => Dimension (M2 a)

Fractional a => SquareMatrix (M2 a)

Num a => Pointwise (M2 a)

Fractional a => Ring (M2 a)

Fractional a => MultSemiGroup (M2 a)

Num a => AbelianGroup (M2 a)

Num a => Tensor (M2 a) (V2 a)

Transpose (M2 a) (M2 a)

Num a => Diagonal (V2 a) (M2 a)

Fractional a => RightModule (V2 a) (M2 a)

Num a => LeftModule (M2 a) (V2 a)

data M3 a

Constructors

M3 !(V3 a) !(V3 a) !(V3 a)

Instances

Num a => Vector a M3

Fractional a => Orthogonal a M3 Ortho3

Num a => Extend a M3 M4

Num a => Extend a M2 M3

Fractional a => Projective a V3 M3 Ortho3 M4 Proj4

Fractional a => Projective a V2 M2 Ortho2 M3 Proj3

Num a => Determinant a (M3 a)

Floating a => MatrixNorms a (M3 a)

Read a => Read (M3 a)

Show a => Show (M3 a)

(Num a, Storable a) => Storable (M3 a)

(Num a, Random a) => Random (M3 a)

Num a => Dimension (M3 a)

Fractional a => SquareMatrix (M3 a)

Num a => Pointwise (M3 a)

Fractional a => Ring (M3 a)

Fractional a => MultSemiGroup (M3 a)

Num a => AbelianGroup (M3 a)

Num a => Tensor (M3 a) (V3 a)

Transpose (M3 a) (M3 a)

Num a => Diagonal (V3 a) (M3 a)

Fractional a => RightModule (V3 a) (M3 a)

Num a => LeftModule (M3 a) (V3 a)

data M4 a

Constructors

M4 !(V4 a) !(V4 a) !(V4 a) !(V4 a)

Instances

Num a => Vector a M4

Fractional a => Orthogonal a M4 Ortho4

Num a => Extend a M3 M4

Num a => Extend a M2 M4

Fractional a => Projective a V3 M3 Ortho3 M4 Proj4

Num a => Determinant a (M4 a)

Floating a => MatrixNorms a (M4 a)

Read a => Read (M4 a)

Show a => Show (M4 a)

(Num a, Storable a) => Storable (M4 a)

(Num a, Random a) => Random (M4 a)

Num a => Dimension (M4 a)

Num a => SquareMatrix (M4 a)

Num a => Pointwise (M4 a)

Num a => Ring (M4 a)

Num a => MultSemiGroup (M4 a)

Num a => AbelianGroup (M4 a)

Num a => Tensor (M4 a) (V4 a)

Transpose (M4 a) (M4 a)

Num a => Diagonal (V4 a) (M4 a)

Num a => RightModule (V4 a) (M4 a)

Num a => LeftModule (M4 a) (V4 a)

data M2x3 a

Constructors

M2x3 !a !a !a !a !a !a

Instances

Read a => Read (M2x3 a)

Show a => Show (M2x3 a)

Storable a => Storable (M2x3 a)

Transpose (M3x2 a) (M2x3 a)

Transpose (M2x3 a) (M3x2 a)

data M2x4 a

Constructors

M2x4 !a !a !a !a !a !a !a !a

Instances

Read a => Read (M2x4 a)

Show a => Show (M2x4 a)

Storable a => Storable (M2x4 a)

Transpose (M4x2 a) (M2x4 a)

Transpose (M2x4 a) (M4x2 a)

data M3x2 a

Constructors

M3x2 !a !a !a !a !a !a

Instances

Read a => Read (M3x2 a)

Show a => Show (M3x2 a)

Storable a => Storable (M3x2 a)

Transpose (M3x2 a) (M2x3 a)

Transpose (M2x3 a) (M3x2 a)

data M3x4 a

Constructors

M3x4 !a !a !a !a !a !a !a !a !a !a !a !a

Instances

Read a => Read (M3x4 a)

Show a => Show (M3x4 a)

Storable a => Storable (M3x4 a)

Transpose (M4x3 a) (M3x4 a)

Transpose (M3x4 a) (M4x3 a)

data M4x2 a

Constructors

M4x2 !a !a !a !a !a !a !a !a

Instances

Read a => Read (M4x2 a)

Show a => Show (M4x2 a)

Storable a => Storable (M4x2 a)

Transpose (M4x2 a) (M2x4 a)

Transpose (M2x4 a) (M4x2 a)

data M4x3 a

Constructors

M4x3 !a !a !a !a !a !a !a !a !a !a !a !a

Instances

Read a => Read (M4x3 a)

Show a => Show (M4x3 a)

Storable a => Storable (M4x3 a)

Transpose (M4x3 a) (M3x4 a)

Transpose (M3x4 a) (M4x3 a)

data Ortho2 a

Orthogonal matrices.

Note: the Random instances generates orthogonal matrices with determinant 1 (that is, orientation-preserving orthogonal transformations)!

Instances

Fractional a => Orthogonal a M2 Ortho2

Fractional a => Projective a V2 M2 Ortho2 M3 Proj3

Num a => Determinant a (Ortho2 a)

Read a => Read (Ortho2 a)

Show a => Show (Ortho2 a)

(Num a, Storable a) => Storable (Ortho2 a)

(Floating a, Ord a, Random a) => Random (Ortho2 a)

Num a => Dimension (Ortho2 a)

Fractional a => SquareMatrix (Ortho2 a)

Fractional a => MultSemiGroup (Ortho2 a)

Transpose (Ortho2 a) (Ortho2 a)

data Ortho3 a

Instances

Fractional a => Orthogonal a M3 Ortho3

Fractional a => Projective a V3 M3 Ortho3 M4 Proj4

Num a => Determinant a (Ortho3 a)

Read a => Read (Ortho3 a)

Show a => Show (Ortho3 a)

(Num a, Storable a) => Storable (Ortho3 a)

(Floating a, Ord a, Random a) => Random (Ortho3 a)

Num a => Dimension (Ortho3 a)

Fractional a => SquareMatrix (Ortho3 a)

Fractional a => MultSemiGroup (Ortho3 a)

Transpose (Ortho3 a) (Ortho3 a)

data Ortho4 a

Instances

Fractional a => Orthogonal a M4 Ortho4

Num a => Determinant a (Ortho4 a)

Read a => Read (Ortho4 a)

Show a => Show (Ortho4 a)

(Num a, Storable a) => Storable (Ortho4 a)

(Floating a, Ord a, Random a) => Random (Ortho4 a)

Num a => Dimension (Ortho4 a)

Fractional a => SquareMatrix (Ortho4 a)

Num a => MultSemiGroup (Ortho4 a)

Transpose (Ortho4 a) (Ortho4 a)

data Proj3 a

Projective matrices, encoding affine transformations in dimension one less.

Instances

Fractional a => Projective a V2 M2 Ortho2 M3 Proj3

Read a => Read (Proj3 a)

Show a => Show (Proj3 a)

(Num a, Storable a) => Storable (Proj3 a)

Fractional a => SquareMatrix (Proj3 a)

Fractional a => MultSemiGroup (Proj3 a)

Transpose (Proj3 a) (Proj3 a)

data Proj4 a

Instances

Fractional a => Projective a V3 M3 Ortho3 M4 Proj4

Read a => Read (Proj4 a)

Show a => Show (Proj4 a)

(Num a, Storable a) => Storable (Proj4 a)

Fractional a => SquareMatrix (Proj4 a)

Num a => MultSemiGroup (Proj4 a)

Transpose (Proj4 a) (Proj4 a)